In this study, aeroelastic analysis of a plate subjected to the external supersonic airflow is carried out. A 3-D rectangular plate element of variable thickness based on absolute nodal coordinate formulation (ANCF) has been developed for the structural model. In the approach to the problem, a continuum mechanics approach for the definition of the elastic forces within the finite element is considered. Both shear strain and transverse normal strain are taken into account. Linearized first-order potential (piston) theory is coupled with the structural model to account for pressure loading. Aeroelastic equations using ANCF are derived and solved numerically. Values of critical dynamic pressure are obtained by a modal approach, in which the mode shapes are obtained by ANCF. All the formulations and the computations are built up in a FORTRAN 90 computer program after it was confirmed by Mathematica®, ver. 5. The results of free vibration analysis and flutter are compared with the available references and reasonable good agreement has been found. However, some results indicate that the known problem of locking (ANCF with uniform thickness) still persist in the current developed formulation.